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Erschienen in:
2015 | OriginalPaper | Buchkapitel
Stability results for the Brunn-Minkowski inequality
verfasst von : Alessio Figalli
Erschienen in: Colloquium De Giorgi 2013 and 2014
Verlag: Scuola Normale Superiore
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The Brunn-Miknowski inequality gives a lower bound on the Lebesgue measure of a sumset in terms of the measures of the individual sets. This classical inequality in convex geometry was inspired by issues around the isoperimetric problem and was considered for a long time to belong to geometry, where its significance is widely recognized. However, it is by now clear that the Brunn-Miknowski inequality has also applications in analysis, statistics, informations theory, etc. (we refer the reader to [29] for an extended exposition on the Brunn-Minkowski inequality and its relation to several other famous inequalities).